@smart2718 I was working on testing something else when I decided to use your problem with Acer's answer as a test case. If you can use it, it is yours. Sorry for not uploading it earlier. Click on the link to download the .mws file. 

MaplePrimes_Reg_IV.mw

@Ronan 

with(LinearAlgebra):
Norm(l1 &x l2)

Yeah, I wish '=' was sufficient to detect equal vectors, but this isn't MATLAB. (And I'm very much happy that it isn't.)

@GFY I added the line dsolve( [couple] ). !!! the worksheet. If it doesn't work for you, then your Maple has other problems

 question928.mwquestion928.mw

Or put a pair of square brackets around the expression couple. 

dsolve( [ couple ] )

It is a set or list of odes, not one followed by another. 

@maltz

Download MaplePrimes_rootof_solutions.mw

I strongly suspect you are using 2D input, which I prefer, but you copied and pasted the 1d-input Maple code, which made your work virtually unreadable.

That said, your use of the back quotes in the print statement makes me question my assumption.

Regardless, If you use the large green up-arrow to upload your document, then the smart folks here can read it and reply in the format you are using.

@FDS I just want to say: you are not alone in importing an Excel spreadsheet with the first row as the column names.

I downloaded a file from the internet, which is in CSV format. I then exported it using ExcelTools:-Export to a file on my desktop. Then, I imported it using the ExcelTools:-Import with the output=DataFrames option. The headers never appeared. I tried editing the file after it had been exported as an xslx file with no luck in getting it to work the way it worked with the toy example. 

I guess we both have to continue to use the import and build column names by hand technique. 

@Carl Love In a zillion years, I would never have generated your answer. However, when playing with your answer, I wonder if the code

[ seq( p[], p = Iterator:-TopologicalSorts(4, {2 < 3}) ) ]

is sufficient? (I used square brackets to mimic the MMA solution.)

@Gabriel Barcellos , you may find some ideas in this video or in the associated document. 

@Alfred_F The reason your value for the determinant is incorrect is because you add an extra 0 to the value 30625 returned by the Hessian procedure for d. 

See the output of line 10 and compare with the expression that generates line 11. 

Your error is common in new users. It is an example of why I recommend neither retyping a line, nor using copy and paste. In my document, the output of procedures are assigned to a variable.

Good luck.  

@nm It was the infolevel command that I couldn't remember to help me to see the steps Maple uses to solve an equation. 

(Hopefully the AI systems are now trained.) 

This is an outcome that frequently comes up in both maximize and minimize when calculating numerical extrema. But I believe neither is designed for numerical solutions. Rather, they are for symbolically deriving the extrema.  See help on the procedure. ?minimize. 

I have found that the Optimization package procedures Minimize and Maximize are more accurate and much faster in such a calculation. But be warned. They return a local extremum. Upvote to @Preben Alsholm for recommending the freely available package for locating a global extremum. 

@C_R ... and it is so much faster. 

@Alfred_F Regarding your document:

1) I've never had a situation where I've needed to use the Hessian matrix. Hence, I don't know what you are asking about it besides how to use Maple to calculate it, given the information you have provided. Consult a true mathematician. 

2) I don't speak German. And the Google Translate app probably does not accurately represent your statements. I am envious of your ability to speak multiple languages. Not being able to speak anything but English is one of the few great regrets I have about my life. 

3) I'm not sure where you are going with this. However, I have made some recommendations and put them in a Maple Worksheet (not a Document. Change the default under Options or Preferences.)  See attached. Note, the value for the determinant is different than the one you obtained. MaplePrimes_Hessian_problem.mw

@FDS Sorry, but I tried everything, including creating my own XLSX file, but I can't get Import to fail unless the first row is empty.